Then how can A be a group?

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## 2 Answers

Best answer

$\begin{array}{c|cc}

⊗&0&1\\ \hline

0&0&0\\

1&0&1

\end{array}$

**a.** $1$ is the identity element. Inverse does not exist for zero. So, it is not a group.

**b.** $\begin{array}{c|cc}

⊗&1&3\\ \hline

1&1&3\\

3&3&1

\end{array}\qquad\begin{array}{c|cc}

⊗&1&5\\\hline1&1&5\\

5&5&1

\end{array}\qquad\begin{array}{c|cc}

⊗&1&7\\\hline1&1&7\\

7&7&1

\end{array}$